The Paraxial Approximation to the Wave Equation in Curvilinear Coordinates for Numerical Simulation of Optical Beam Diffraction

摘要

As a rule, problems on the propagation of optical waves in homogeneous are inhomogeneous media, including the computation of eigenmodes of dielectric waveguides and cavity resonators, can be reduced to the solution of the Helmholtz equation or the parabolic approximation to this equation [1, 2]. Both the statement of the problem and its subsequent analysis are simplified dramatically in a coordinate system in which the inhomogeneities of the medium are arranged in the directions of coordinate axes [3, 4]. In a number of practically interesting cases, for example, in simulation wedge- and cone-shaped waveguides, the adaptation of the coordinate system to the inhomogeneities can be implemented with the use of the corresponding standard orthogonal curvilinear coordinates.